Digital networks generally involve the modulation of a digital message on a transmitted signal. Typically, digital messages are encoded prior to modulation and transmission, and decoded upon reception and de-modulation. The encoded digital messages are generally grouped into one or more bits forming a symbol. The symbol is used to select a high-frequency, sinusoidal electromagnetic (EM) wave that has been identified as representing the symbol. The technique generally used to transmit a symbol by a high frequency sinusoidal EM wave is to alter the wave's amplitude, frequency, and/or phase in a designated manner. Therefore, an EM wave comprising a predetermined amplitude, frequency, and/or phase represents a symbol, i.e., a predetermined bit pattern.
Upon reception, the EM wave is demodulated and decoded to determine the digital message. Generally, particularly in the use of a turbo decoder in a system utilizing Quadrature Amplitude Modulation (QAM), a demodulator generates a soft output of the log likelihood that a particular bit is a one or a zero. The turbo decoder uses the log likelihood as input to the turbo decoder algorithm. The log likelihood, however, is a time-consuming and processing-intensive calculation that generally involves multiple comparators and multipliers
Therefore, there is a need for a method and an apparatus for determining the log likelihood ratio that a bit in a received digital message is a one verses that it is a zero.